Garcia, 28, became the first qualifier to win a WTA 1000 title with her 6-2 6-4 win against Petra Kvitova.
In the men's final, Coric, the world number 152, became the lowest-ranked player to claim a Masters Trophy.
He beat Greek fourth seed Stefanos Tsitsipas 7-6 (7-0) 6-2.
The previous holder of the record was then-world number 143 Roberto Carretero of Spain, who won in Hamburg in 1996.
Coric has been as high as 12th in the ATP rankings but was absent for a year with a shoulder injury and only returned to the circuit in March.
He beat British number one Cameron Norrie in Saturday's semi-final after earlier dispatching Rafael Nadal and Felix Auger-Aliassime.
Garcia's win saw her claim the third Masters Trophy of her career after back-to-back successes in Wuhan and Beijing almost five years ago.
The world number 35 is now set to return to the top 20 rankings for the first time since 2017.
After getting through qualifying, Garcia beat three top-10-ranked opponents in Maria Sakkari, Aryna Sabalenka and Jessica Pegula, before another superb performance against Czech two-time Wimbledon champion Kvitova.
No qualifier had won a WTA 1000 title since the tier was created in 2009.
Garcia, who leads the WTA Tour in aces and is second in break points saved, played to her strengths to triumph in one hour and 42 minutes.
She served 11 aces and saved all eight break points she faced for her third title of the year after earlier successes on clay in Warsaw and on grass in Bad Homburg.
Garcia's record of 33 victories in total this year is bettered only by Iga Swiatek (50), Simona Halep (39) and Ons Jabeur (38).